Re: Cartesian morphism ~~> fibration

I'm trying to find a reference for the following result, if indeed it is true.

I think the claim is wrong in general. Let P : X->B be a fibration of categories with a terminal object, i.e. P has a right adjoint right inverse One. Then One : Id_B -> P is a cartesian functor though itself not a fibration in general (e.g. B = 1 and X the ordinal 2 then One picks 1 from 2 which has empty fibre over 0). However, if P is a fibration and Q is a discrete fibration and F is a functor with QF = P then F is a fibration iff F is a cartesian functor from P to Q. Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]